reserve A,X for non empty set;
reserve f for PartFunc of [:X,X:],REAL;
reserve a for Real;

theorem Th21:
  for X being non empty set, f being PartFunc of [:X,X:],REAL,
      x being Element of X st f is Reflexive discerning holds
   [x,x] in low_toler(f,0)
proof
  let X be non empty set, f be PartFunc of [:X,X:],REAL, x be Element of X;
  assume f is Reflexive discerning;
  then f.(x,x) = 0 by METRIC_1:def 2;
  hence thesis by Def3;
end;
